Intuition has always been associated with a hint of the anomalous, with credible examples of intuitive knowledge that appear to arise from the future or from distant locations without sensory mediation. Experimental and anecdotal evidence exists to suggest that a complete understanding of intuition will need to include these anomalous aspects of intuition. To that end it is important to recognize that an understanding of anomalous intuition, though presenting considerable challenges to physics and neuroscience, may not require ‘paranormal’ explanations or entities outside the compass of science. Anomalous intuition has traditionally been studied within the field of parapsychology where is it known as extrasensory perception (ESP). One model of ESP proposes two stages. In the first stage, the process, the anomalous information is ‘received’ and in the second stage, the product, the anomalous information is elaborated into conscious awareness and/or behaviour. The process is a challenge primarily for physics, and physicists both within parapsychology and in the mainstream are addressing it. The product, anomalous intuition, is grounded in normal psychological activity and is a problem for psychology and neuroscience to understand. In order to understand how ESP or anomalous intuition works, it is necessary to understand its purpose within an evolutionary context. Evolution has proven exceptionally effective in enabling species to make use of a wide range of physical phenomena for information gathering and communication. If some yet undiscovered physical process permits retrocausation would we not expect evolution to have capitalized on that process. As a product of evolution, ESP would have to conform to the requirements of evolutionary theory. Suddendorf and Corballis (2007) have elaborated the notion of mental time travel (MTT), the memory-based ability to project oneself into the past as well as the future, and have argued that the “ultimate evolutionary advantage” may lie in the capacity to envisage future events. Their model of MTT provides an ideal context in which to understand an evolutionary path for anomalous intuition. Working through the emotional system, anomalous intuition may operate by influencing the selection of memory images we use to execute our MTT. A growing body of data supports the involvement of the emotional system in anomalous intuition but there is only suggestive evidence for the expected hereditary component. The observed limited effectiveness of anomalous intuition may emerge from the balance achieved through an evolutionarily stable strategy, or result from inherent limitations in capitalizing on the underlying physical process